They blame the game. They don't state the child's mentality. She was said to have kicked the dog. How else was she abusive to it? Could she have been screaming, or acting hostile before sitting down to play the ds? Children, especially as they grow older, can be outright twits in this generation - swearing, bullying, not listening to their parents. Many can also feel invulnerable to the world due to a lack of punishment.
So who's to say that she was simply sitting there playing the ds when, suddenly and out of nowhere, the bull mastiff comes up and mauls her? Maybe she was screamed at by her parents to sit down and stay out of the way of trouble, then waved the DS threateningly at the dog. Or barking as loud and annoyingly as she could with the dogs on the DS to see how the dog would react.
There could have been other circumstances that we weren't aware of. Normally if a child is bitten by a family dog, it's the child's fault for antagonizing the animal and thinking they can get away with it. The parents and family will never admit to the news that their kid is a brat or little prick. The news will only go after pictures for shock value, and try to find the strangest wedge in the story to follow instead of looking for the truth. What sounds more interesting? Little girl beats on dog and is mauled? Or Little girl plays ds and dog attacks her because of the game?
Additionally, well, what everyone else has been saying. The dog may have not been trained well around little girls. Perhaps it had previous attack incidents we aren't aware of. Usually a dog attack has rules behind it, like if the dog previously did nothing outwardly aggressive it is allowed a second chance with restrictions. Though the owners could have put it down on a personal family rule of 'dog bites kid, dog is shot out back.' in which it wouldn't matter how well loved the dog is.
edit - I'm curious on, if the dog was possibly upset by the ds, why it didn't just take the ds and eat it instead going head on and tearing the kid up.